Geodesic
On subgroups that cover only $\mathfrak F$-central chief factors in finite groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 158-163
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The authors call an element $x$ of a finite group $G$ $Q\mathfrak F$-supercentral if every chief factor $A/B$ of $G$ for which $x\in A\backslash B$ is $\mathfrak F$-central. The connection between $Q\mathfrak F$-supercentral elements of $G$ and its chief factors is investigated. In the case when $\mathfrak F$ is a nonempty saturated formation, the properties of subgroups that cover all $\mathfrak F$-central chief factors of $G$ and isolate all $\mathfrak F$-eccentric chief factors are investigated (the authors call these subgroups $\mathfrak F$-isolators). The connection between $\mathfrak F$-isolators and $\mathfrak F$-normalizers of $G$ is established.
Keywords: finite group, saturated formation, $Q\mathfrak F$-supercentral element, $\mathfrak F$-normalizer, $\mathfrak F$-isolator. 
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S. F. Kamornikov; O. L. Shemetkova. On subgroups that cover only $\mathfrak F$-central chief factors in finite groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 158-163. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a15/

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